(x-1)(x-2)(x-2)-(x-1)=0

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Solution for (x-1)(x-2)(x-2)-(x-1)=0 equation: 


Simplifying
(x + -1)(x + -2)(x + -2) + -1(x + -1) = 0

Reorder the terms:
(-1 + x)(x + -2)(x + -2) + -1(x + -1) = 0

Reorder the terms:
(-1 + x)(-2 + x)(x + -2) + -1(x + -1) = 0

Reorder the terms:
(-1 + x)(-2 + x)(-2 + x) + -1(x + -1) = 0

Multiply (-1 + x) * (-2 + x)
(-1(-2 + x) + x(-2 + x))(-2 + x) + -1(x + -1) = 0
((-2 * -1 + x * -1) + x(-2 + x))(-2 + x) + -1(x + -1) = 0
((2 + -1x) + x(-2 + x))(-2 + x) + -1(x + -1) = 0
(2 + -1x + (-2 * x + x * x))(-2 + x) + -1(x + -1) = 0
(2 + -1x + (-2x + x2))(-2 + x) + -1(x + -1) = 0

Combine like terms: -1x + -2x = -3x
(2 + -3x + x2)(-2 + x) + -1(x + -1) = 0

Multiply (2 + -3x + x2) * (-2 + x)
(2(-2 + x) + -3x * (-2 + x) + x2(-2 + x)) + -1(x + -1) = 0
((-2 * 2 + x * 2) + -3x * (-2 + x) + x2(-2 + x)) + -1(x + -1) = 0
((-4 + 2x) + -3x * (-2 + x) + x2(-2 + x)) + -1(x + -1) = 0
(-4 + 2x + (-2 * -3x + x * -3x) + x2(-2 + x)) + -1(x + -1) = 0
(-4 + 2x + (6x + -3x2) + x2(-2 + x)) + -1(x + -1) = 0
(-4 + 2x + 6x + -3x2 + (-2 * x2 + x * x2)) + -1(x + -1) = 0
(-4 + 2x + 6x + -3x2 + (-2x2 + x3)) + -1(x + -1) = 0

Combine like terms: 2x + 6x = 8x
(-4 + 8x + -3x2 + -2x2 + x3) + -1(x + -1) = 0

Combine like terms: -3x2 + -2x2 = -5x2
(-4 + 8x + -5x2 + x3) + -1(x + -1) = 0

Reorder the terms:
-4 + 8x + -5x2 + x3 + -1(-1 + x) = 0
-4 + 8x + -5x2 + x3 + (-1 * -1 + x * -1) = 0
-4 + 8x + -5x2 + x3 + (1 + -1x) = 0

Reorder the terms:
-4 + 1 + 8x + -1x + -5x2 + x3 = 0

Combine like terms: -4 + 1 = -3
-3 + 8x + -1x + -5x2 + x3 = 0

Combine like terms: 8x + -1x = 7x
-3 + 7x + -5x2 + x3 = 0

Solving
-3 + 7x + -5x2 + x3 = 0

Solving for variable 'x'.

The solution to this equation could not be determined.

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